scholarly journals ANALISIS KESTABILAN MODEL MATEMATIKA JUMLAH PEROKOK PENGARUH KENAIKAN HARGA ROKOK DENGAN DINAMIKA AKAR KUADRAT

2020 ◽  
Vol 9 (4) ◽  
pp. 283
Author(s):  
FIDELIS NOFERTINUS ZAI ◽  
ARYL ZULDAUS SEMBIRING ◽  
ARDINAL VANBASTEN ◽  
ANGGI NOVITA NASUTION ◽  
LASKER PANGARAPAN SINAGA
Keyword(s):  
Mathematical Model ◽  
Single Point ◽  
Endemic Equilibrium ◽  
Square Root ◽  
Asymptotically Stable ◽  
Root Dynamics ◽  
The Public ◽  
Long Period ◽  
The Mathematical Model ◽  
Heavy Smokers

Consumption of cigarettes in large quantities by the public is one of the main concerns in every country because cigarettes contain harmful ingredients that can trigger various diseases. This journal will explain the mathematical model of the number of smokers affected by rising prices of cigarettes with square root dynamics. The population is divided into four, composed of potential smokers, occasionally smokers, heavy smokers, and ex-smokers. The results of the model analysis are that there is a single point of smoker’s endemic equilibrium. If conditions are met, then the endemic equilibrium point of smokers will be asymptotically stable, and over a long period of time there will always be a spread of smokers.

MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

2021 ◽  
Vol 5 (10) ◽  
Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
The Mathematical Model ◽  
Globally Stable ◽  
Well Posed ◽  
The Basic Reproduction Number ◽  
Invariant Principle

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

scholarly journals An Approach for the Global Stability of Mathematical Model of an Infectious Disease

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1778
Author(s):  
Mojtaba Masoumnezhad ◽  
Maziar Rajabi ◽  
Amirahmad Chapnevis ◽  
Aleksei Dorofeev ◽  
Stanford Shateyi ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Global Stability ◽  
Incidence Rates ◽  
Endemic Equilibrium ◽  
Symmetry Properties ◽  
Nonlinear Incidence Rates ◽  
Lyapunov Matrix ◽  
The Stability ◽  
The Mathematical Model

The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.

scholarly journals A Mathematical Model of a Tuberculosis Transmission Dynamics Incorporating First and Second Line Treatment

2020 ◽  
Vol 24 (5) ◽  
pp. 917-922
Author(s):  
J. Andrawus ◽  
F.Y. Eguda ◽  
I.G. Usman ◽  
S.I. Maiwa ◽  
I.M. Dibal ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Line Treatment ◽  
Second Line ◽  
Tuberculosis Transmission ◽  
Disease Free

This paper presents a new mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment. We calculated a control reproduction number which plays a vital role in biomathematics. The model consists of two equilibrium points namely disease free equilibrium and endemic equilibrium point, it has been shown that the disease free equilibrium point was locally asymptotically stable if thecontrol reproduction number is less than one and also the endemic equilibrium point was locally asymptotically stable if the control reproduction number is greater than one. Numerical simulation was carried out which supported the analytical results. Keywords: Mathematical Model, Biomathematics, Reproduction Number, Disease Free Equilibrium, Endemic Equilibrium Point

scholarly journals Modeling Transmission of Tuberculosis with MDR and Undetected Cases

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Yongqi Liu ◽  
Zhendong Sun ◽  
Guiquan Sun ◽  
Qiu Zhong ◽  
Li Jiang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Control Strategies ◽  
Multidrug Resistant ◽  
Vital Role ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Tb Control ◽  
Disease Free

This paper presents a novel mathematical model with multidrug-resistant (MDR) and undetected TB cases. The theoretical analysis indicates that the disease-free equilibrium is globally asymptotically stable ifR0<1; otherwise, the system may exist a locally asymptotically stable endemic equilibrium. The model is also used to simulate and predict TB epidemic in Guangdong. The results imply that our model is in agreement with actual data and the undetected rate plays vital role in the TB trend. Our model also implies that TB cannot be eradicated from population if it continues to implement current TB control strategies.

scholarly journals Analisis Kestabilan dan Kontrol Optimal Model Matematika Penyebaran Penyakit Ebola dengan Penanganan Medis

2019 ◽  
Vol 1 (1) ◽  
pp. 19
Author(s):  
Sofita Suherman ◽  
Fatmawati Fatmawati ◽  
Cicik Alfiniyah
Keyword(s):  
Optimal Control ◽  
Medical Treatment ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
The Stability ◽  
The Mathematical Model ◽  
Treatment Population ◽  
Deceased Individual ◽  
Two Equilibria

Ebola disease is one of an infectious disease caused by a virus. Ebola disease can be transmitted through direct contact with Ebola’s patient, infected medical equipment, and contact with the deceased individual. The purpose of this paper is to analyze the stability of equilibriums and to apply the optimal control of treatment on the mathematical model of the spread of Ebola with medical treatment. Model without control has two equilibria, namely non-endemic equilibrium (E0) and endemic equilibrium (E1) The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is locally asymptotically stable if  R0 < 1 and endemic equilibrium tend to asymptotically stable if R0 >1 . The problem of optimal control is then solved by Pontryagin’s Maximum Principle. From the numerical simulation result, it is found that the control is effective to minimize the number of the infected human population and the number of the infected human with medical treatment population compare without control.

Approbation of the Mathematical Model of Adhesive Strength with Viscoelasticity

2019 ◽  
Vol 816 ◽  
pp. 96-101
Author(s):  
Stepan V. Litvinov ◽  
Xuan Zhen Song ◽  
Serdar B. Yazyev ◽  
Artur Avakov
Keyword(s):  
Mathematical Model ◽  
Adhesive Strength ◽  
Adhesive Joint ◽  
Epoxy Resins ◽  
Polymeric Materials ◽  
Critical Value ◽  
Structural Elements ◽  
Long Period ◽  
Tangential Stresses ◽  
The Mathematical Model

Expressed viscoelasticity of polymeric materials which can develop over a long period of time prevents their widespread. Some types of polymers, such as epoxy resins, can be used to connect various structural elements. The destruction in this case can be caused by the growth of tangential stresses in the adhesive joint and their achievement of some critical value τadhezive, at which the adhesive joint is destroyed.

scholarly journals ABOUT METHODS OF THE SUBSTANTIATION OF AN ALLOWABLE RISK LEVEL

2000 ◽  
Vol 6 (1) ◽  
pp. 60-65
Author(s):  
Anatoly V. Perelmuter
Keyword(s):  
Mathematical Model ◽  
Linear Dependence ◽  
Risk Estimation ◽  
Risk Level ◽  
The Public ◽  
Actual Risk ◽  
Life Saving ◽  
Points Of View ◽  
Public Reaction ◽  
The Mathematical Model

The problem of admissible risk optimisation is described in detail, especially for the case of possible human victims. Different points of view on the problem of «human being cost» are compared, and the approach based on comparing the numbers of saved lives and the risk for the persons, providing the life saving are considered. An information on actual risk level for different kinds of human activities is presented. The mathematical model of creating the public opinion in case of accidents and analysis of changing the function of society discomposibility function in time are presented. Effects commonly ignored during risk estimation are analysed—like departure from the principle of equal providing the risks for objects of equal responsibility, but different quantity and presence of non-linear dependence between the severity of accidents and public reaction.

scholarly journals Stability Analysis of Mathematical Models of the Dynamics of Spread of Meningitis with the Effects of Vaccination, Campaigns and Treatment

2020 ◽  
Vol 17 (1) ◽  
pp. 71-81
Author(s):  
Sulma Sulma ◽  
Syamsuddin Toaha ◽  
Kasbawati Kasbawati
Keyword(s):  
Infectious Disease ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Vaccination Campaign ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Infected People ◽  
The Stability ◽  
Vaccination Campaigns ◽  
The Mathematical Model

Meningitis is an infectious disease caused by bacteria, viruses, and protosoa and has the potential to cause an outbreak. Vaccination and campaign are carried out as an effort to prevent the spread of meningitis, treatment reduces the number of deaths caused by the disease and the number of infected people. This study aims to analyze and determine the stability of equilibrium point of the mathematical model of the spread of meningitis using five compartments namely susceptibles, carriers, infected without symptoms, infected with symptoms, and recovered with the effect of vaccination, campaign, and treatment. The results obtained from the analysis of the model that there are two equilibrium points, namely non endemic and endemic equilibrium points. If a certain condition is met then the non endemic equilibrium point will be asymptotically stable. Numerical simulations show that the spread of disease decreases with the influence of vaccination, campaign, and treatment.

Analisis Model Matematika Penyebaran Penyakit Demam Berdarah Dengue dengan Treatment

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Mohammad Soleh ◽  
Zulpikar Zulpikar ◽  
Ari Pani Desvina
Keyword(s):  
Mathematical Model ◽  
Dengue Virus ◽  
Equilibrium State ◽  
Human Body ◽  
Hemorrhagic Fever ◽  
Asymptotically Stable ◽  
And Control ◽  
The Mathematical Model ◽  
Endemic Equilibrium State

Demam Berdarah Dengue (DBD) adalah penyakit yang disebabkan oleh virus Dengue yang ditularkan ke tubuh manusia melalui gigitan nyamuk Aedes aegypti. Pasien yang terinfeksi virus memerlukan perawatan. Perawatan adalah metode yang penting dan efektif untuk mencegah dan mengendalikan penyebaran penyakit. Dalam makalah ini, kami membahas tentang analisis model matematika dari penularan demam berdarah dengan pengobatan. Studi ini meneliti model Esteva-Vargas yang dimodifikasi menggunakan pengobatan fungsi Wang. Hasil penelitian mengungkapkan bahwa ada satu kondisi kesetimbangan dari endemisitas penyakit. Jika pengobatan dilakukan dengan k<0,000186 kondisi kesetimbangan endemik penyakit stabil asimptotik, dan dalam jangka panjang akan selalu terjadi penyebaran penyakit. Sedangkan jika pengobatan dengan k≥0,000186 keadaan kesetimbangan endemik penyakit tidak stabil asimptotik, dan dalam jangka panjang akan bebas dari penyakit.   Dengue Hemorrhagic Fever (DHF) is a disease caused by Dengue virus that is transmitted to human body through AedesAegypti mosquito bites. Patients infected with the virus require treatment. treatment is an important and effective method to prevent and control the spread of disease. In this paper discusses about the mathematical model analysisof transmission dengue fever with treatment.This study examined the modified Esteva-Vargas model using the treatment of the Wang function. The results obtained, there is one disease endemic equilibrium state. If the treatment with k<0,000186then diseaseendemic equilibrium state is asymptotically stable, and in the long term will always happen deployment disease. Whereas if the treatment with k≥0,000186 then diseaseendemic equilibrium state is not asymptotically stable, and in the long term will always happen freedisease.

scholarly journals Experience in modeling a comfortable environment in the transport compartment

2020 ◽  
Vol 157 ◽  
pp. 01019
Author(s):  
Vladimir Pankratov ◽  
Alexey Golikov ◽  
Elena Pankratova ◽  
Marina Barulina ◽  
Sofiya Galkina
Keyword(s):  
Mathematical Model ◽  
Operating Conditions ◽  
Temperature Fields ◽  
Thermal Processes ◽  
Passenger Compartment ◽  
The Public ◽  
Actual Operating ◽  
Specific Proposal ◽  
Series Of Experiments ◽  
The Mathematical Model

The theoretical base was developed and the mathematical model of dynamic thermal processes in a compartment of public transport was constructed. The software which is realized the constructed mathematical model was developed. The mathematical model provides for the possibility of taking into account the most possible environmental conditions which can have place in the actual operating conditions of a transport even the angle of illumination - the current temperature of the external environment, the presence of solar radiation taking into account the angle of sun’s illumination, and the temperature of the roadway. The software allows calculation and visualization non –stationary temperature fields in the public transport’s compartments using the example of a trolley bus. For a specific trolley bus design, a series of experiments to calculate the comfortable temperature for passengers were conducted, These experiments are showed the performance of the constructed model and allowed to formulate a specific proposal for improving the thermoregulation system of the trolleybus’ passenger compartment.

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